Abstract

We give a new construction of the
q-extensions of Euler numbers and polynomials. We present new
generating functions which are related to the q-Euler numbers and
polynomials. We also consider the generalized q-Euler polynomials
attached to Dirichlet's character χ and have the generating
functions of them. We obtain distribution relations for the
q-Euler polynomials and have some identities involving q-Euler
numbers and polynomials. Finally, we derive the q-extensions of
zeta functions from the Mellin transformation of these generating
functions, which interpolate the q-Euler polynomials at negative
integers.